A subset of a real or complex vector space is balanced whenA nonempty balanced set contains zero, is invariant under multiplication by scalars of modulus one and contains the segment from zero to each of its points. Balance is often called circled in the complex setting.
Every centered norm ball is balanced, by homogeneity of the norm. In , the union of the two coordinate-axis unit segments is balanced but not convex: it contains and but not their midpoint. Thus radial scalar closure does not imply closure under arbitrary convex combinations.
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The term "balanced set" can refer to different concepts in various fields, but it often implies a situation or collection that is equalized or organized in a way that maintains fairness or proportionality. Here are a few contexts in which the term might be used: 1. **Mathematics and Statistics**: In statistics, a balanced set may refer to a data set where the distribution of categories or groups is even.